Unit 8, Lesson 6
Finding Side Lengths of Triangles
Accelerated 7
Preparation
Lesson Narrative
In this lesson students investigate relationships between the side lengths of right and non-right triangles, leading to the Pythagorean Theorem.
Students begin by comparing aspects of 4 triangles purposefully chosen to prime them to think about patterns. In the next activities, students notice patterns between the side lengths of right and non-right triangles and the areas of squares that share a side length with the right and non-right triangles (MP8). Students learn that the legs of a right triangle are the sides that make the right angle and the hypotenuse is the side of a right triangle that is opposite the right angle. By the end of this lesson, they see that for right triangles only, given legs
- Comprehend the term “Pythagorean Theorem” (in written and spoken language) as the equation
, where and are the lengths of the legs, and is the length of the hypotenuse of a right triangle.
Required Preparation
None
hypotenuse
The hypotenuse is the side of a right triangle that is opposite the right angle. It is the longest side of a right triangle.
Here are some right triangles. Each hypotenuse is labeled.
legs
The legs of a right triangle are the sides that make the right angle.
Here are some right triangles. Each leg is labeled.
Pythagorean Theorem
The Pythagorean Theorem describes the relationship between the side lengths of right triangles.
The square of the hypotenuse is equal to the sum of the squares of the legs. This is written as
This diagram shows the relationship.
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